Simplify; express your answer in exponential form. Assume $n\neq 0, y\neq 0$. $\dfrac{{n^{5}}}{{(n^{5}y^{3})^{-2}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${n^{5} = n^{5}}$ In the denominator, we can use the distributive property of exponents. ${(n^{5}y^{3})^{-2} = (n^{5})^{-2}(y^{3})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{n^{5}}}{{(n^{5}y^{3})^{-2}}} = \dfrac{{n^{5}}}{{n^{-10}y^{-6}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}}}{{n^{-10}y^{-6}}} = \dfrac{{n^{5}}}{{n^{-10}}} \cdot \dfrac{{1}}{{y^{-6}}} = n^{{5} - {(-10)}} \cdot y^{- {(-6)}} = n^{15}y^{6}$.